You should understand that upgrading items is NOT based on fixed costs but on a randomize success roll.

The higher you level up your artifacts, the higher the costs will also be.

So it could be that you need only a few hundred k to level up an artifact to 16...it could also be you need 2-3 million silver. 

It is a randomized approach...

Oh, and never buy silver with gems...buy energy and run spider dungeons to sell the unwanted accessoires...

silver  is a huge resource to manage correctly in this game

to level up 1 piece of gear from lvl 1 to lvl 16 you can expect to spend between 1.5 and 2.5  million silver  on average / on a bad day maybe closer to 3 million

silver can be easily farmed  in the game with energy  by running campaign 12/3 brutal 100s  of times while leveling up champions then selling all that gear (shields)

Another favorite to farm is the Spider Dungeon and selling unwanted loot as well as these  items will give the  most silver  but a tougher component of the game to farm for   newer accounts

experienced  players do not buy silver. They farm it as a general rule as  its easy to farm 10s  of  millions  of silver  in just a few  hrs  of  game play

There is a nonzero chance that there is some fishy "IF goldamount > X THEN" but most likely its just bad rng, jewellery upgrades cost more than armor upgrades and can chew through gold faster than fat kid through cookie store